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Questionable Logic

 
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Thu Jul 01, 2010 7:51 pm    Post subject: Questionable Logic Reply with quote

Here is the code after basics for Danny's puzzle 10/07/01: VH.

Code:
+-------------+------------+-----------------+
| 3  4   1    | 26  5   8  | 7     9   26    |
| 8  26  7    | 246 1   9  | 246   5   3     |
| 9  26  5    | 7   3   46 | 18    246 18    |
+-------------+------------+-----------------+
| 46 7   2    | 1   46  3  | 5     8   9     |
| 46 1   3    | 8   9   5  | 246   246 7     |
| 5  89  89   | 46  2   7  | 3     1   46    |
+-------------+------------+-----------------+
| 1  589 4689 | 3   468 46 | 24689 7   24568 |
| 7  58  468  | 9   468 2  | 1468  3   14568 |
| 2  3   4689 | 5   7   1  | 4689  46  468   |
+-------------+------------+-----------------+

Play this puzzle online at the Daily Sudoku site

Note the two AURs: AUR 89 in r67c23 & AUR 18 in r38c79
Both of these two AURs create a pseudocell (456)

Looking at the AUR 18 we make the following observations:
1. The pseudocell in r8c79 can be viewed as (46=5)
2. The contents of r9c9 can be viewed as (8=46)
3, Thus a short chain may be formed: (8=46)r9c9 - (46=5)r8c79 - (5=8)r8c2; r8c79,r9c3<>8

A similr step is possible for AUR 89.

Question: Is my logic valid?

Ted
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Thu Jul 01, 2010 9:46 pm    Post subject: Re: Questionable Logic Reply with quote

tlanglet wrote:
Looking at the AUR 18 we make the following observations:
1. The pseudocell in r8c79 can be viewed as (46=5)
2. The contents of r9c9 can be viewed as (8=46)
...

In order to have a pair of candidates on one or both sides of a strong inference, there has to be a pair of cells. R9c9 is a single cell, so it obviously doesn't qualify. The r8c79 pseudocell is a pair of cells that behaves like a single cell, so it doesn't qualify either.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Jul 01, 2010 10:28 pm    Post subject: Reply with quote

ronk wrote:
In order to have a pair of candidates on one or both sides of a strong inference, there has to be a pair of cells.

Good point!

Ted: you need an ALS relationship.

(8=46)r9c89 - UR(46=5)r8c79 - (5=8)r8c2; r8c79,r9c3<>8
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Jul 02, 2010 10:17 am    Post subject: Reply with quote

daj95376 wrote:
ronk wrote:
In order to have a pair of candidates on one or both sides of a strong inference, there has to be a pair of cells.

Ted: you need an ALS relationship.

(8=46)r9c89 - UR(46=5)r8c79 - (5=8)r8c2; r8c79,r9c3<>8

I didn't think this exeption would surface so quickly. Surprised For the pseudocell r8c79, we have the valid strong inference (46=5) r8c79 with a pair of candidates on one side of the inference. A pseudocell behaves like a single cell, so how is this possible?

A pseudocell with three candidates is effectively an AALS, and an AALS may be doubly-linked to an ALS. In this context "doubly-linked" means there are two "restricted commons." As written, there is an implied logical 'and' (&) between the candidates ...

(8=4&6)r9c89 - UR(4&6=5)r8c79

... at least when read left-to-right. Written below in the opposite direction, there is an implied logical 'or' (|) between the candidates ...

(5=4|6)r8c79 - (4|6=8)r9c89
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Fri Jul 02, 2010 11:58 am    Post subject: Reply with quote

Ron & Danny,

Thanks for the feedback. I need to chew on the info some more to (hopefully?) understand it since my fundamentals are still weak.

In fact, when I first saw the two patterns, I formed as ALS using the bivalue (46) in r7c6 and r9c8 respectively. However while preparing to post that solution, I got thinking about the alternate and decided to post it instead.

Thanks again..........

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Jul 02, 2010 3:36 pm    Post subject: Reply with quote

ronk wrote:
I didn't think this exeption would surface so quickly. Surprised For the pseudocell r8c79, we have the valid strong inference (46=5) r8c79 with a pair of candidates on one side of the inference. A pseudocell behaves like a single cell, so how is this possible?

A pseudocell with three candidates is effectively an AALS, and an AALS may be doubly-linked to an ALS. In this context "doubly-linked" means there are two "restricted commons." As written, there is an implied logical 'and' (&) between the candidates ...

(8=4&6)r9c89 - UR(4&6=5)r8c79

... at least when read left-to-right. Written below in the opposite direction, there is an implied logical 'or' (|) between the candidates ...

(5=4|6)r8c79 - (4|6=8)r9c89

Yes, what a mess we end up with when compact expressions are used in notation. Let's write this thing out and reduce some of the clutter.

First: UR(4|5|6)r8c79 is my interpretation -- non-exclusive "or"

Second: als is really (8)r9c9 = (46)r9c89 -- thus the need for two cells

Leaving a left-to-right of:

(8)r9c9 = (46)r9c89 - UR(4|6=5)r8c79

Leaving a right-to=left of:

UR(5=4|6)r8c79 - (46)r9c89 = (8)r9c9

I give others credit for understanding the compact notation on the als, and I give them credit for understanding what is meant when I drop the (|) designator in the UR:

(8=46)r9c89 - UR(46=5)r8c79

I don't want to think of how many &'s and |'s you'd need to explain the left-to-right and right-to-left interpretations of Luke's last als term here. I still get nightmares from when Myth Jellies insisted on including the logical operators in his expressions! _ Very Happy
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Jul 02, 2010 5:24 pm    Post subject: Reply with quote

daj95376 wrote:
I give others credit for understanding the compact notation on the als, and I give them credit for understanding what is meant when I drop the (|) designator in the UR:

(8=46)r9c89 - UR(46=5)r8c79

I don't want to think of how many &'s and |'s you'd need to explain the left-to-right and right-to-left interpretations of ...

My detailing the logic of doubly-linking an AALS to an ALS is certainly not the same as suggesting logical '&' and '|' symbols be used in most AICs. Did I say that? Do I otherwise post AICs using the symbols? Did I not use twice use the word "implied"?

Besides, beyond producing clutter, over half the people using the symbols would just get it wrong, like you did when ...

you wrote:
Leaving a left-to-right of:

(8)r9c9 = (46)r9c89 - UR(4|6=5)r8c79
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Jul 02, 2010 6:03 pm    Post subject: Reply with quote

ronk wrote:
Besides, beyond producing clutter, over half the people using the symbols would just get it wrong, like you did when ...

you wrote:
Leaving a left-to-right of:

(8)r9c9 = (46)r9c89 - UR(4|6=5)r8c79


Hmmmmm!!! When I was taking logic, they taught us that:

not( A or B) ==>> not(A) and not(B)

Now, if I take my expression "- UR(4|6=5)r8c79" and spread the not operator across the operand containing the or operator, then I get the following logical expression:

If r8c79 does not contain <4> and r8c79 does not contain <6>, then r8c9 must contain <5>.

Regards, Danny

[Edit: replaced r8c79=5 with r8c9=5, and removed unnecessary comment.]


Last edited by daj95376 on Fri Jul 02, 2010 9:54 pm; edited 1 time in total
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Jul 02, 2010 7:46 pm    Post subject: Reply with quote

daj95376 wrote:
ronk wrote:
Besides, beyond producing clutter, over half the people using the symbols would just get it wrong, like you did when ...

you wrote:
Leaving a left-to-right of:

(8)r9c9 = (46)r9c89 - UR(4|6=5)r8c79


Hmmmmm!!! When I was taking logic, they taught us that:

not( A or B) ==>> not(A) and not(B)

Believe it or not, I do understand Boolean logic and I understand your POV. Maybe we should change the AIC notation name to AIBE (Alternating Inference Boolean Expression). Smile I tend to look at chain notation as an inference stream, not a Boolean expression. That's probably also why I still prefer nice-loop notation for chains, where the above would look like ...

-8- r9c89 -46- UR:r8c79 -5-

Then it's '4&6' reading left-to-right and '4|6' reading right-to-left, without question. IOW r9c89 holds 4 and 6 reading L2R, r8c79 holds 4 or 6 reading R2L.

BTW there's no need to yell.
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Fri Jul 02, 2010 11:59 pm    Post subject: Reply with quote

ronk wrote:
daj95376 wrote:
not( A or B) ==>> not(A) and not(B)

BTW there's no need to yell.

I'm sorry if it seemed like yelling. I'm accustomed to seeing mathematical expressions in bold.
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